1. Field of the Invention
This invention relates to seismic-data processing and particularly to a method of improving the resolution of migration in sections having steeply-dipping reflector horizons.
2. Discussion of the Related Art
In reflection seismic profiling, seismic signals are generated at or near the surface of the earth. Normally these seismic signals are considered to be in the form of a compressional wave field. As the signals propagate downward into the earth they are reflected and diffracted by discontinuities in the earth. Some of the signals are returned upward to the surface of the earth where they are detected by suitable seismic sensors. The returned signals are usually in the form of a train of seismic waves that are received over a predetermined period of time such as 10 seconds (s).
Along the earth's surface above an area of interest, many sensors are deployed along a line or grid. Each sensor is usually in the form of an electromechanical transducer which converts the detected seismic signals into corresponding electrical signals. The electrical signals generated by each sensor correspond in amplitude and phase as a function of frequency to that of the received seismic wave train. The electrical signals from each sensor are transmitted over conductors to a remote recording unit for later processing.
The detected seismic signals do not provide a true cross-section of the earth's subsurface. They represent only the two-way travel time of the signals generated at the earth's surface to a reflector and back to the surface. The reflected signals reaching the surface propagate in the form of ever-expanding wave fronts. In a non-uniform medium, variations in velocity of propagation tend to influence and modify the direction of propagation and are accompanied by mutual interference of wave fronts. In zones of sudden changes along geologic interfaces such as faults, a portion of the seismic signal undergoes diffraction. Consequently the record of detected signals represents a distorted image of the earth's subsurface; an image which has undergone a complicated process of focusing, defocusing, interference and diffraction. A numerical process for correcting these propagation effects in the data is the process of migration.
Migration is the process used to transform received seismic data into a visual display more closely representative of the subsurface. One migration technique that has been widely used is founded on the finite-difference formulation of the scalar-wave equation. The finite-difference approach relies on the separation of upgoing and downgoing signals by approximations to a differential equation. This approach requires a correct propagation velocity, V, to fully migrate the seismic data. This approach, although sufficiently accurate for reflectors having dips less than about 25 degrees, does not work well with seismic data where reflectors have dips greater than about 25 degrees.
The migration error, a combination of incorrect positioning of reflectors and frequency-dependent dispersion, is a complicated function of many parameters: the temporal and spatial sampling intervals associated with the discretely-sampled data, the depth increment used in the finite-difference approximation to the derivative with respect to depth, the medium velocity, seismic-signal frequency, and reflector dip. A major source of migration error is an error in the estimate of the migration velocity. The effects of an incorrect choice of migration velocity increase somewhat exponentially with the reflector dip and the magnitude of the velocity used in the migration calculation. In general, with proper choices of parameters, the position error (usually expressed in terms of relative error in lateral position or time), is generally less than 1% for dips less than 20 degrees and more than 5% for dips greater than 25 degrees. For dips greater than 35 degrees, the error exceeds 10% and the method becomes useless. While other migration approaches (e.g., frequency-wavenumber and Kirchhoff-summation migration) are more accurate under restricted conditions, the finite-difference method is the most efficient of the methods capable of migrating data from media on which the velocity varies vertically and horizontally.